Online Learning for Load Balancing of Unknown Monotone Resource Allocation Games

Ilai Bistritz*, Nicholas Bambos

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Consider N players that each uses a mixture of K resources. Each of the players' reward functions includes a linear pricing term for each resource that is controlled by the game manager. We assume that the game is strongly monotone, so if each player runs gradient descent, the dynamics converge to a unique Nash equilibrium (NE). Unfortunately, this NE can be inefficient since the total load on a given resource can be very high. In principle, we can control the total loads by tuning the coefficients of the pricing terms. However, finding pricing coefficients that balance the loads requires knowing the players' reward functions and their action sets. Obtaining this game structure information is infeasible in a large-scale network and violates the users' privacy. To overcome this, we propose a simple algorithm that learns to shift the NE of the game to meet the total load constraints by adjusting the pricing coefficients in an online manner. Our algorithm only requires the total load per resource as feedback and does not need to know the reward functions or the action sets. We prove that our algorithm guarantees convergence in L2 to a NE that meets target total load constraints. Simulations show the effectiveness of our approach when applied to smart grid demand-side management or power control in wireless networks.

Original languageEnglish
Title of host publicationProceedings of the 38th International Conference on Machine Learning, ICML 2021
PublisherML Research Press
Pages968-979
Number of pages12
ISBN (Electronic)9781713845065
StatePublished - 2021
Externally publishedYes
Event38th International Conference on Machine Learning, ICML 2021 - Virtual, Online
Duration: 18 Jul 202124 Jul 2021

Publication series

NameProceedings of Machine Learning Research
Volume139
ISSN (Electronic)2640-3498

Conference

Conference38th International Conference on Machine Learning, ICML 2021
CityVirtual, Online
Period18/07/2124/07/21

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